#### 34.3.1 Defining Indexing And Indexed Assignment

Objects can be indexed with parentheses or braces, either like `obj(idx)` or like `obj{idx}`, or even like `obj(idx).field`. However, it is up to the programmer to decide what this indexing actually means. In the case of the polynomial class `p(n)` might mean either the coefficient of the n-th power of the polynomial, or it might be the evaluation of the polynomial at n. The meaning of this subscripted referencing is determined by the `subsref` method.

: subsref (val, idx)

Perform the subscripted element selection operation on val according to the subscript specified by idx.

The subscript idx must be a structure array with fields ‘type’ and ‘subs’. Valid values for ‘type’ are `"()"`, `"{}"`, and `"."`. The ‘subs’ field may be either `":"` or a cell array of index values.

The following example shows how to extract the first two columns of a matrix

```val = magic (3)
⇒ val = [ 8   1   6
3   5   7
4   9   2 ]
idx.type = "()";
idx.subs = {":", 1:2};
subsref (val, idx)
⇒ [ 8   1
3   5
4   9 ]
```

Note that this is the same as writing `val(:, 1:2)`.

If idx is an empty structure array with fields ‘type’ and ‘subs’, return val.

For example, this class uses the convention that indexing with `"()"` evaluates the polynomial and indexing with `"{}"` returns the n-th coefficient (of the n-th power). The code for the `subsref` method looks like

```function r = subsref (p, s)

if (isempty (s))
error ("@polynomial/subsref: missing index");
endif

switch (s(1).type)

case "()"
idx = s(1).subs;
if (numel (idx) != 1)
error ("@polynomial/subsref: need exactly one index");
endif
r = polyval (fliplr (p.poly), idx{1});

case "{}"
idx = s(1).subs;
if (numel (idx) != 1)
error ("@polynomial/subsref: need exactly one index");
endif

if (isnumeric (idx{1}))
r = p.poly(idx{1}+1);
else
r = p.poly(idx{1});
endif

case "."
fld = s.subs;
if (! strcmp (fld, "poly"))
error ('@polynomial/subsref: invalid property "%s"', fld);
endif
r = p.poly;

otherwise
error ("@polynomial/subsref: invalid subscript type");

endswitch

if (numel (s) > 1)
r = subsref (r, s(2:end));
endif

endfunction
```

The equivalent functionality for subscripted assignments uses the `subsasgn` method.

: subsasgn (val, idx, rhs)

Perform the subscripted assignment operation according to the subscript specified by idx.

The subscript idx must be a structure array with fields ‘type’ and ‘subs’. Valid values for ‘type’ are `"()"`, `"{}"`, and `"."`. The ‘subs’ field may be either `":"` or a cell array of index values.

The following example shows how to set the two first columns of a 3-by-3 matrix to zero.

```val = magic (3);
idx.type = "()";
idx.subs = {":", 1:2};
subsasgn (val, idx, 0)
⇒  [ 0   0   6
0   0   7
0   0   2 ]
```

Note that this is the same as writing `val(:, 1:2) = 0`.

If idx is an empty structure array with fields ‘type’ and ‘subs’, return rhs.

: val = optimize_subsasgn_calls ()
: old_val = optimize_subsasgn_calls (new_val)
: optimize_subsasgn_calls (new_val, "local")

Query or set the internal flag for `subsasgn` method call optimizations.

If true, Octave will attempt to eliminate the redundant copying when calling the `subsasgn` method of a user-defined class.

When called from inside a function with the `"local"` option, the variable is changed locally for the function and any subroutines it calls. The original variable value is restored when exiting the function.

Note that the `subsref` and `subsasgn` methods always receive the whole index chain, while they usually handle only the first element. It is the responsibility of these methods to handle the rest of the chain (if needed), usually by forwarding it again to `subsref` or `subsasgn`.

If you wish to use the `end` keyword in subscripted expressions of an object, then there must be an `end` method defined. For example, the `end` method for the polynomial class might look like

```function r = end (obj, index_pos, num_indices)

if (num_indices != 1)
error ("polynomial object may only have one index");
endif

r = length (obj.poly) - 1;

endfunction
```

which is a fairly generic `end` method that has a behavior similar to the `end` keyword for Octave Array classes. An example using the polynomial class is then

```p = polynomial ([1,2,3,4]);
p{end-1}
⇒ 3
```

Objects can also be used themselves as the index in a subscripted expression and this is controlled by the `subsindex` function.

: idx = subsindex (obj)

Convert an object to an index vector.

When obj is a class object defined with a class constructor, then `subsindex` is the overloading method that allows the conversion of this class object to a valid indexing vector. It is important to note that `subsindex` must return a zero-based real integer vector of the class `"double"`. For example, if the class constructor were

```function obj = myclass (a)
obj = class (struct ("a", a), "myclass");
endfunction
```

then the `subsindex` function

```function idx = subsindex (obj)
idx = double (obj.a) - 1.0;
endfunction
```

could be used as follows

```a = myclass (1:4);
b = 1:10;
b(a)
⇒ 1  2  3  4
```

Finally, objects can be used like ranges by providing a `colon` method.
This function is equivalent to the operator syntax `base : limit` or `base : increment : limit`.